Cauchys Derivative Formula

Hi.

Evaluate the integral with respect to C, C={ z: lz+2l = 3}, Integrate cos(pi*z)/( ((z+4)^2)*(z-2).dz

I understand that from the denominator the value -4 lies inside C but the point 2 does not.

Am i right in thinking then f(z)=(cos(pi*z)) / ((z-2)^2) is analytic on R and C is a simple closed contour in R. Hence by Cauchy's First Derivative Formula......

....and this is where I'm unsure.

Any suggestions?

Shoni

If there is a singularity in your region, then no, it is not a simple closed contour. You will need to evaluate residues.

What does that mean exactly to "evaluate the residues?" Please could you show me using the example?

Thanks Prove It!